For your date formatting...

$min = "0" . $min if (length($min) == 1);

... I would recommend using sprintf instead:

$min = sprintf "%02d", $min;

For your date calculations (adding one time value to another), you can do it much more succinctly with Date::Calc.

print@_{sort keys %_},$/if%_=split//,'= & *a?b:e\f/h^h!j+n,o@o;r$s-t%t#u'